Nuclear Physics - Nuclear instability and Radius

Question 1

Where on N/Z graph are alpha, beta plus and beta minus emitters found

Answer 1

Alpha - near the top of the line of stability
Beta minus - to the left of the line of stability
Beta plus - to the right of line of stability

Question 2

When is a nucleus unstable

Answer 2

If it has too many:

Protons
Neutrons
Nucleons
Energy

Question 3

N/Z graphs and stability for light isotopes with Z<20

Answer 3

Nuclei tend to be stable
Follow straight line N=Z

Question 4

What must happen for heavy isotopes with Z>20 to be stable

Answer 4

The neutron-proton ratio increases
Stable nuclei must have more neutrons than protons

Question 5

What happens in the nucleus at a short range of 1-3fm

Answer 5

Nucleons are bound by the strong nuclear force

Question 6

What happens below 1fm

Answer 6

The strong nuclear force is repulsive in order to prevent the nucleus from collapsing

Question 7

What happens at longer ranges in the nucleus

Answer 7

The electromagnetic force acts between protons and so more protons cause more instability

Question 8

Why must more neutrons be added when more protons are added to the nucleus

Answer 8

To add distance between protons to reduce the electrostatic repulsion. The extra neutrons also increase the amount of binding force which helps to bind the nucleons together

Question 9

where does electron capture occur on an N/Z graph

Answer 9

To the right of the stability line as the isotopes are proton rich

Question 10

Which decay occurs when there are too many neutrons and what happens

Answer 10

Beta minus occurs
Neutron number decreases by 1
Proton number increases by 1

Question 11

Equation for beta minus

Answer 11

neutron → proton + beta minus particle (electron) + antinuetrino

Question 12

Which decay occurs when there are too many protons

Answer 12

Beta plus or electron capture occurs
Nucleon number stays constant
Neutron number increases by 1
Proton number decreases by 1

Question 13

What happens in beta plus decay

Answer 13

A proton changes into a neutron and a beta plus particle (positron) and a neutrino are released

Question 14

What happens in electron capture

Answer 14

An orbiting electron is taken in by the nucleus and combined with a proton. This forms a neutron and a neutrino

Question 15

Which decay occurs when there are too many nucleons and what happens

Answer 15

Alpha emission occurs
Nucleon number decreases by 4
Both proton and neutron number decrease by 2

Question 16

Which decay occurs when there is too much energy and what happens

Answer 16

Gamma emission occurs
This is usually after a different decay as the nucleus becomes too excited and has excess energy

Question 17

How can you calculate and find out which decay occurs

Answer 17

Calculate the neutron:nucleon ratio or the neutron:proton ratio.
The more neutron rich nucleus with higher ratio undergoes beta minus etc….

Question 18

What happens when a daughter nucleus is in an excited state

Answer 18

Emits remaining energy in the form of a gamma photon.
The nucleus quickly moves to its ground state either directly or via one or more lower energy excited states

Question 19

What is the application of nuclear excited states

Answer 19

use of technetium-99m as a γ source in medical diagnosis.

Question 20

What does the m in technetium-99m stand for

Answer 20

metastable - which means the nucleus exists in a particularly stable excited state

Question 21

Which two ways can nuclear radius be measured

Answer 21

Rutherford scattering - closest approach method
Electron scattering

Question 22

Describe the closest approach method

Answer 22

The alpha particle is fired at a thin sheet of gold foil with an initial KE.
The Rutherford scattering indicates there must be an electrostatic repulsion between alpha p and gold nucleus
At the point of closest approach, r, the repulsive force reduces the speed of alpha particles to 0 momentarily.

So initial KE of alpha particles is transferred to electric potential energy.

Question 23

Equation for electric potential energy

Answer 23

EPE = charge1 x charge2 / 4pi x e0 x radius of closest approach

Question 24

What does using KE = EPE to find nuclear radii assume

Answer 24

Assuming the alpha particle is fired at high energy

Question 25

What does the closest approach method give

Answer 25

An estimate of the upper limit of the radius of the nucleus

Question 26

Advantages of the closest approach method

Answer 26

Alpha scattering gives good estimate of upper limit for nuclear radius
Simple maths
Alpha particles are scattered only by protons and not all the nucleons in the nucleus

Question 27

Disadvantages of the closest approach method

Answer 27

Does not give accurate value for radius as it is always an overestimate
Alpha particles contain hadrons which are affected by strong nuclear force
Gold nucleus will recoil as alpha particle approaches
Alpha particles have finite size whereas electrons can be treated as a point mass
Foil must be very thin to prevent multiple scattering
Alpha particles assumed to have same initial KE

Question 28

What is the wave-like property of electrons

Answer 28

The ability to diffract

Question 29

de Broglie wavelength of an electron =

Answer 29

Planck’s constant / mass of an electron x speed of electron

Question 30

What does the equation for the de Broglie wavelength of an electron show

Answer 30

As the speed of the electron increases, the smaller the wavelength becomes

Question 31

Describe what happens when a beam of electrons is directed at a thin target

Answer 31

Each electron will diffract around a nucleus.
A diffraction pattern is formed consisting of a central bright spot with dimmer concentric circles around it.

Question 32

How can we find the size of the nucleus using the electron diffraction pattern

Answer 32

Plot a graph of intensity against diffraction angle.
Use the angle of first minimum intensity to determine size of nucleus

Question 33

What are the advantages of electron scattering

Answer 33

More accurate than closest approach method
Gives direct measurement of the radius of a nucleus
Electrons are leptons so are not affected by strong nuclear force

Question 34

Disadvantages of electron scattering

Answer 34

Electrons must be accelerated to very high speeds to maximise resolution as significant diffraction occurs when wavelength is similar size to nucleus.

Electrons can be scattered by both protons and neutrons and excessive scattering can make first minimum difficult to determine

Question 35

actual radius of gold nucleus

Answer 35

6.6fm

Question 36

Equation to find nuclear radius from electron scattering

Answer 36

sin theta = 1.22 x ( de Broglie wavelength / 2 x radius )

Question 37

how to find nuclear radius from closest approach method

Answer 37

KE = EPE
rearrange to find r
remember the mass = 4u = 4 x mass of a proton

Question 38

How does a graph of nuclear radius against nucleon number look

Answer 38

Graph starts with steep gradient at origin
Gradient decreases gradually to almost horizontal

Question 39

What does the graph of nuclear radius against nucleon number show

Answer 39

As more nucleons added, nucleus gets bigger
Number of nucleons is not proportional to its size

Question 40

What does the radius of nuclei depend on

Answer 40

The nucleon number because a more nucleons added, more space is occupied by nucleus so has a larger radius

Question 41

Equation showing the relationship between radius and nucleon number

Answer 41

Nuclear radius = R0 x nucleon number ^ 1/3

Question 42

Show that the density of a nucleus is constant and independent of the radius

Answer 42

V = 4/3 x pi x r^3

R = R0 x A^1/3

V = 4/3 x pi x R0^3 x A

density = m/v

m= = Au

density = Au / (4/3 x pi x R0^3 x A) = 3u / 4 x pi x R0^3

mass number A cancels out and remaining quantities are all constant

Question 43

What does the nuclear density being significantly larger than atomic density suggest

Answer 43

Majority of atoms mass is in the nucleus
Nucleus is very small compared to the atom
Atoms must be mostly empty space